Let U = {7, 8, 9, 10, 11, 12, 13}, A = {7, 8, 9, 10}, B = {7, 8, 11, 12}, and C = {9, 11, 13}. List all the members of the given set.
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A ∪ (B ∩ C)
B ∩ C = {11} ----> all those found in B AND C
so A ∪ {11} = {7,8,9,10,11} ---> all those found in either A OR {11}
sometimes it helps to "verbalize" it, using
"and " for ∩
"or" for ∪
so if there is a line above set a as a complement a , then would the anwser be
{11,12,13}?
yes, think of the complement as NOT A
To find the union of set A with the intersection of sets B and C, you need to perform the following steps:
1. Find the intersection of sets B and C: B ∩ C
- B ∩ C = {7, 8} (since these are the elements that are common to both sets B and C)
2. Find the union of set A with the result from step 1: A ∪ (B ∩ C)
- A ∪ (B ∩ C) = {7, 8, 9, 10} ∪ {7, 8}
- To find the union, you combine all the distinct elements from both sets without duplicating any element.
After combining the sets, the final set would be: {7, 8, 9, 10}
Therefore, the members of the given set A ∪ (B ∩ C) are: 7, 8, 9, and 10.